Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1424 |
| Sylow | C5 ⋊ #67576 |
| Sylow | C3 ⋊ #10598067 |
112 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=ceg,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,h^b=h^2,i^b=i^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5432);